7/14/2015
Modeling of MR-guided HIFU for
Breast and Brain Therapy
Douglas Christensen
Department of Bioengineering
Department of Electrical & Computer Engineering
University of Utah
Salt Lake City, UT 84112
Utah Center for Advanced Imaging Research
Outline of Talk
• Overview of Hybrid Angular Spectrum (HAS)
method
• Three examples of use:
1. Modeling of acoustic radiation force imaging
(ARFI)
2. Determining extent of phase aberration in
breast treatments
3. Predicting heating efficiency in transcranial
treatments (on-going)
Concept of Hybrid Angular Spectrum Method*
• Extends traditional angular spectrum method (in
spatial-frequency domain) to include inhomogeneous
media
• Leapfrogs between the space and spatial-frequency
domains (next slide)
• Employs FFT commands, so very rapid
• Assumptions: steady state conditions, linearity and
compressional waves only
*U. Vyas and D. A. Christensen, "Ultrasound beam simulations in inhomogeneous tissue
geometries using the hybrid angular spectrum method," IEEE Trans UFFC 59 (6), 10931100, June 2012.
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equivalent thin layers
space domain
a1, r1
c1
transducer
pt
RayleighSommerfeld
integral
p0
transfer
through
plane 1
transfer
through
plane 2
p1-
p2-
ETC.
inhomogeneous
tissue
a2, r2
c2
p1
propagation
direction
plane 1
plane
plane22
A1-(a,b)
plane
plane33
plane
planen…
n…
FFT-1
FFT
spatial-frequency
domain
(angular spectrum)
A1(a,b)
linear propagation filter
HAS Method Overview
• Comparable to FDTD results within 2.8% (3D breast model)*
• Two orders of magnitude faster*:
FDTD – 67 min
HAS – 9.6 s
3D pressure pattern:
• Example simulation:
wedge
3.5 MHz
beam 
3D model 141 x 141 x 161
absorbing
cylinder
*U. Vyas and D. A. Christensen, IEEE Trans UFFC
59 (6), 1093-1100, June 2012.
HAS gui Screen Shot with Typical Pressure Pattern
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Example 1 – ARFI Modeling
Study by Allison Payne with Josh de Bever et al.*
Uses –
• Finding location of beam focus in any tissue
(e.g., replaces thermal test shot in fatty tissue)
• Determining mechanical properties of tissue
(e.g., for treatment assessment)
*A. Payne, J. de Bever, A. Farrer, B. Coats, D. Parker and D. Christensen, "A simulation
technique for 3D MR-guided acoustic radiation force imaging," Med. Phys. 21(2), Feb 2015.
Origin of Radiation Force
Fabs =
2a I
c
Fref =
2IR 2
c
Ftot
é
3ù
ëêN m ûú
é
2ù
ëêN m ûú
I = intensity from HAS calculation
a = tissue absorption coefficient
R = interface reflection coefficient
c = speed of sound
Ftot = Dx DyDz Fabs + Dx Dy Fref [ N]
Generation of Displacement w due to Distributed Force
Simplifications: Poisson’s
Homogeneous
Elastostatic
ratio
medium
≈
medium
0.5 so l >> m
g(r)
Ftot
z
w
r
w
distributed
force field
1  z2 1
    Ftot
8m  r 3 r 
l = first Lame coefficient
m = Lame shear coefficient
• 3D green’s function g(r) is convolved with distributed force field
(computed using the HAS technique)
• Carried out in frequency domain
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Experimental Validation with MRI
• Three different values of gelatin
stiffness (Young’s modulus) used: 125,
175 and 250 bloom
MEG
gelatin
phantom
45-mm
30-mm
water
bath
z
x
ultrasound
transducer
• Young’s modulus, speed of sound and
attenuation independently measured
(similar to soft tissue values)
• Displacement in 3D volume
determined by MR phase
measurements*
• Ultrasound on for 10 ms at 66 W.
* J. de Bever, N. Todd, M. Diakite, D. Parker, Proceedings of the ISMRM
21st Scientific Meeting, Salt Lake City, USA, 20–26 Apr., 2013.
Results – Displacement for 125 bloom
experiment
theory
µm
transverse
µm
longitudinal
Results – All three bloom values
Notes:
• Peak displacement
inversely related to
Young’s modulus (bloom
value)
experimental
simulated
125-bloom
175-bloom
• Displacement shape
broadens for faster
shear wave speed
(higher Lame coefficient)
250-bloom
transverse slice, 30-mm focus depth
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Example 2 – Determining Extent of
Phase Aberration in Breast Treatments
Study by Allison Payne with Alexis Farrer and Chris Dillon et al.*
Motivation –
• Phase aberration is a known issue in HIFU with large-aperture
transducers (e.g., transcranial)
• Extent of phase aberration is unknown for smaller aperture
transducers (e.g., Utah breast system)
*A. Farrer, S. Almquist, C. Dillon, D. Parker, D. Christensen and A. Payne, “Phase aberration
simulation study of MRgFUS breast treatments,” 15th International Symposium on
Therapeutic Ultrasound, Utrecht, Apr. 15-18, 2015
Utah MRgFUS Breast System
phased-array
transducer
Goals of Breast Study
•
Determine if phase aberrations will be present for our
smaller aperture transducer through HAS-simulated
treatments
•
Investigate how the treatment will benefit from phase
aberration correction in the presence of various degrees
of breast heterogeneity
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MRI Patient Data
4 female volunteers with
fibroadenoma(s)
Patient 1
Patient 2
Patient 3
Patient 4
• 18 to 45 years old
• 1 to 8 fibroadenomas
per patient
• 3-point Dixon
acquisition
• Contrast-enhanced
T1-weighted images
Segmentation
T1-w
Water-only
Fat-only
Segmented anatomy
fibroadenoma
breast fat
skin
fibroglandular
tissue
silicone
nipple cover
water
Acoustic Simulations
• Acoustic properties
determined from Duck et al.
1990*
Speed of Sound
• 0.5-mm isotropic resolution
• Hybrid Angular Spectrum
(HAS) method employed to
give SAR pattern
Attenuation Coefficient
* FA Duck, Physical Properties of Tissues. Academic Press: Harcourt Brace Jovanovich,1990.
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Treatment Simulation Set-Up
Superior Approach
Treatment Simulation Set-Up
Inferior Approach
Treatment Simulation Set-Up
Inferior Approach
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Treatment Simulation Set-Up
Inferior Approach
Treatment Simulation Set-Up
Inferior Approach
Intended Treatment Volume (TV)
TV
1 2 3 4
8 7 6 5
9 10 11 12
16 15 14 13
• Mean run-time:
4 mins on GPU
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Phase Correction Approach
Uncorrected
Corrected Phases
Phases
constructive
interference
Results: Power Deposition
Uncorrected Phases
Corrected Phases
W/m2
5 cm
W/m3
5 cm
Thermal Simulations
Thermal Conductivity
Specific Heat Capacity
• Pennes Bioheat Equation –
FDTD simulation
• Heating: 15 s/location;
no cooling between locations
Pennes Perfusion
• Power output adjusted to
achieve a 20 ˚C rise at first
treatment location
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Results: Thermal Dose*
Uncorrected Phases
Corrected Phases
CEM@
43˚C
CEM@
43˚C
TV
TV
5 cm
5 cm
*S. A. Sapareto and W. C. Dewey, “Thermal dose determination in cancer therapy,” Int. J. Radiat. Oncol.,
Biol., Phys. 10(6), 787–800 (1984).
Dose Volume Ratio Metric
Uncorrected Phases
Corrected Phases
DVR = 9.1
DVR = 3.9
TV
TV
Dose Volume Ratio (DVR):
DVR = Volume Outside TV ≥ 240CEM / Volume Inside TV ≥ 240CEM
(smaller is better)
Results: DVR (Dose Volume Ratio)
14.0
Not Corrected (NC)
Corrected (C)
12.0
Superior Inferior
10.0
0.15
8.0
0.10
6.0
C
NC
Inferior
Inferior
Superior
0.05
Superior
4.0
2.0
Superior
0.00
Patient 1
NC
0.0
Patient 1
Superior
approach
Inferior
C
NC C
Patient 2
NC
C
NC
Patient 3
C
NC
C
NC C
Patient 4
Inferior
approach
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Example 3 – Predicting Heating
Efficiency in Transcranial Treatments
Study by Dennis Parker with Scott Almquist and
Henrik Odeen et al.* (on-going)
Background –
• Temperature profiles (space and time) available for 14 patients
undergoing transcranial essential tremor treatments
• Perform retrospective analysis of temperature as a function of
applied acoustic energy to determine efficiency of heating
*S. Almquist, N. Todd, J. de Bever, D. Parker and D. Christensen, "Correcting Phase
Aberrations in Transcranial High Intensity Focused Ultrasound," International Society for
Therapeutic Ultrasound Symposium, Heidelberg, Germany, June 11-13, 2012.
Modeling of Transcranial Treatments
InSightec 650-kHz ExAblateNeuro
1024-element applicator
in place
Modeling of Transcranial Treatments
Modeling Steps:
Temperature Rise (°C)
clinical temperatures
simulated temperatures
• Model skull from CT scan with acoustic
values based on Hounsfield Units*
• Propagate beam into brain with HAS
using clinically found element
amplitudes and phases
Heating
Efficiency
( °C/J )
Applied Energy (J)
* S. Pichardo, V. W. Sin, and K.
Hynynen, Phys. Med. Biol., 56
(1) 219, Jan 2011
• From HAS SAR pattern, find peak
temperature with bioheat equation
(FDTD)
• Plot peak temperature as a function of
exposure energy: slope = Heating
Efficiency (°C/J)
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Patient 1
Patient 1
Notes:
25
clinical temperatures
simulated temperatures
• Some clinical searching for
optimum temperature
imaging plane
Temperature Rise (°C)
20
15
• Bending over of clinical
plot at higher temperatures
10
• Reasonable simulation
match at lower energy
levels
5
0
0
2000
4000
6000
Applied Energy (J)
8000
10000
Patient 13
Patient 15
Patient 13
Patient 15
25
15
clinical temperatures
simulated temperatures
Temperature Rise (°C)
Temperature Rise (°C)
20
15
10
10
5
5
clinical temperatures
simulated temperatures
0
0
2000
4000
6000
Applied Energy (J)
0
0
8000
Overpredicted
0.5
1
1.5
Applied Energy (J)
2
2.5
x 10
4
Underpredicted
Patient 13
Patient 15
Patient 13
Patient 15
25
15
clinical temperatures
simulated temperatures
Temperature Rise (°C)
Temperature Rise (°C)
20
15
10
10
5
5
clinical temperatures
simulated temperatures
0
0
2000
4000
6000
Applied Energy (J)
Overpredicted
8000
0
0
0.5
1
1.5
Applied Energy (J)
2
2.5
x 10
4
Underpredicted
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Acknowledgements
Allison Payne, PhD
Doug Christensen, PhD
Dennis Parker, PhD
Bob Roemer, PhD
Rock Hadley, PhD
Josh de Bever, PhD
Henrik Odéen, PhD
Chris Dillon, PhD
Alexis Farrer, MS
Robb Merrill,
MS
Thank
You
Emilee Minalga, MS
Scott Almquist, BS
Sara Johnson, BS
Bryant Svedin, BS
Matt Holbrook, BS
Any Questions?
Siemens Healthcare AG
NIH grants:
R01 CA172787
R01 EB013433
Image Guided Therapy
FUS Foundation
Utah Center for Advanced Imaging Research
Thank You
Any Questions?
Utah Center for Advanced Imaging Research
Numerical Modeling of Focused Ultrasound
Uses • Predicting beam and heating patterns
• Determining phases for aberration correction
• Retrospective analysis of treatments
• Designing custom applicators
• Potential for patient treatment planning
Limitations • Only as valid as model parameters
• Simplifications reduce accuracy
• Need experimental validation
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Results – Displacement (µm) for 125 bloom
transverse
longitudinal
30-mm
focus
(N=11)
experimental
simulated
45-mm
focus
(N=5)
Summary – HAS Technique
• HAS method allows rapid beam calculations of
pressure, intensity and SAR patterns.
• Includes refraction, attenuation and reflection
effects.
• MATLAB gui provides convenient user interface.
Future work:
• Including shear waves and multiple reflections.
• Adding scattering component to attenuation.
Summary – ARFI Modeling (Example 1)
• Developed a numerical model for ARFI
displacements
• Force field calculated by the HAS technique
• Validated with 3D MRI displacement
measurements
• Model estimates displacements to within 2.8-12 %
accuracy
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Summary – Breast System (Example 2)
• Phase aberration correction improved most
treatments for our smaller aperture breast
specific system.
• The degree of improvement depends on the
amount of tissue heterogeneity in the beam path.
Future Work:
• Determine a figure of merit for clinicians that
indicates how beneficial patient-specific phase
correction will be.
Summary – Transcranial (Example 3)
• aaa
• Bbb
Future Work:
• ccc
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